cgesl(3P)

NAME

cgesl - solve the linear system Ax = b for a general matrix A, which has been LU- factored by xGECO or xGEFA, and vectors b and x.

SYNOPSIS

CALL DGESL (DA, LDA, N, IPIVOT, DB, JOB)

void cgesl(complex ∗ca, long int lda, long int n, long int ∗ipivot,
complex ∗cb, long int job)

CALL SGESL (SA, LDA, N, IPIVOT, SB, JOB)

CALL ZGESL (ZA, LDA, N, IPIVOT, ZB, JOB)

CALL CGESL (CA, LDA, N, IPIVOT, CB, JOB)

void dgesl(double ∗da, long int lda, long int n, long int ∗ipivot,
double ∗db, long int job)

void sgesl(float ∗sa, long int lda, long int n, long int ∗ipivot, float ∗b, long int
job)

void zgesl(doublecomplex ∗za, long int lda, long int n,
long int ∗ipivot, doublecomplex ∗zb, long int job)

void cgesl(complex ∗ca, long int lda, long int n, long int ∗ipivot,
complex ∗cb, long int job)

ARGUMENTS

xALU factorization of the matrix A, as computed by xGECO or xGEFA.

LDALeading dimension of the array A as specified in a dimension
or type statement. LDA >= max(1,N).

NOrder of the matrix A. N >= 0.

IPIVOTPivot vector as computed by xGECO or xGEFA.

xBOn entry, the right-hand side vector b.
On exit, the solution vector x.

JOBDetermines which operation the subroutine will perform:
0 Solve the system Ax = b.
not 0 Solve the linear system AHx = b. Note that ATx = AHx for real matrices.

SAMPLE PROGRAM

      PROGRAM TEST
      IMPLICIT NONE
C
      INTEGER           IAXEQB, LDA, LDB, N
      PARAMETER        (IAXEQB = 0)
      PARAMETER        (N = 3)
      PARAMETER        (LDA = N)
      PARAMETER        (LDB = LDA)
C
      DOUBLE PRECISION A(LDA,N), B(LDB)
      INTEGER           ICOL, INFO, IPIVOT(N), IROW, JOB
C
      EXTERNAL          DGEFA, DGESL
C
C     Initialize the array A to store the matrix A shown below.
C     Initialize the array B to store the vector b shown below.
C
C         1 2 2        15
C     A = 2 1 2    b = 15
C         2 2 1        15
C
      DATA A / 1.0D0, 3∗2.0D0, 1.0D0, 3∗2.0D0, 1.0D0 /
      DATA B / 3∗1.5D1 /
C
      PRINT 1000
      PRINT 1010, ((A(IROW,ICOL), ICOL = 1, N), IROW = 1, N)
      PRINT 1020
      PRINT 1030, B
      CALL DGEFA (A, LDA, N, IPIVOT, INFO)
      IF (INFO .EQ. 0) THEN
        JOB = IAXEQB
        CALL DGESL (A, LDA, N, IPIVOT, B, JOB)
        PRINT 1040
        PRINT 1030, B
      ELSE
        PRINT 1050, INFO
      END IF
C
1000 FORMAT (1X, ’A:’)
1010 FORMAT (3(3X, F4.1))
1020 FORMAT (/1X, ’b:’)
1030 FORMAT (1X, 2X, F4.1)
1040 FORMAT (/1X, ’A∗∗(-1)∗b’)
1050 FORMAT (1X, ’A appears singular at ’, I2)
C
      END

SAMPLE OUTPUT

A:
    1.0    2.0    2.0
    2.0    1.0    2.0
    2.0    2.0    1.0

b:
   15.0
   15.0
   15.0

A∗∗(-1)∗b
    3.0
    3.0
    3.0